Substrate positioning system

ABSTRACT

A substrate positioning system is provided to facilitate the performing of certain processing on the substrate, such as ion implantation. The system comprises a linkage rotatably mounted to a base and an end effector member rotatably mounted to the linkage and configured for receiving a substrate. Through the synchronized rotation of the linkage about the base and the end effector member about the linkage, the system acts as a robotic unit to move the substrate to the desired location for performing processing thereon. In another aspect, the base is movable along an axis such that the system maintains a constant distance of travel for an ion beam incident on the substrate as the linkage and end effector member travel in a curved path.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/081,610, filed Feb. 20, 2002, entitled “SUBSTRATE POSITIONINGSYSTEM”, now abandoned, which claims priority to U.S. provisional patentapplication serial No. 60/270,644, filed Feb. 20, 2001, entitled “ROBUSTMECHANICAL SCAN ROBOT FOR AN ION IMPLANTER WITH A SINGLE ROTARYLINKAGE”, and are incorporated herein by reference.

BACKGROUND OF THE INVENTION

This invention relates generally to positioning mechanisms, and moreparticularly, to a substrate positioning system facilitating theperforming of certain processing on the substrate, such as ionimplantation.

DESCRIPTION OF RELATED ART

Robotic units and other positioning mechanisms are known for performingcertain controlled tasks. With respect to mechanisms for assisting inion implantation on a substrate, such as a semiconducting wafer, amechanical scanning apparatus has been used in conjunction with ionimplanters to ensure that ion beams incident on the substrate reach thewhole surface area. The ion implanters typically scan the ion beamelectrically in a first axis across the substrate surface and utilizethe mechanical scanning apparatus to scan the substrate mechanicallyalong a second axis perpendicular to the first. The mechanical scan isnecessary due to the difficulty of electrically scanning the beam over alarge area of the substrate while keeping the angle of incidence of thebeam to the substrate surface constant. Additionally, the mechanicalscan must move the substrate at a certain velocity and at the correctangle of incidence as to avoid ion dosage and substrate depthnon-uniformities.

Nogami et al., in U.S. Pat. No. 5,003,183, describe a mechanism thatswings a wafer through the beam by rotating its holder from the side.Although this mechanism maintains a constant impact point of the ionbeam with the wafer tilted at an angle of incidence, the wafer rotationmust be coordinated with the scan to avoid velocity variation across thewafer and resulting ion dosage variations.

Brune et al., in U.S. Pat. No. 5,229,615, describe a two-link robot armfor mechanically scanning a wafer. This device requires the coordinationof three rotary axes to maintain the angle of incidence at a constantvalue as the wafer is scanned, thus adding additional complexity ofmotion.

Thus, what is desired is a substrate positioning system that canaccurately move a substrate to desired positions for performing certainprocessing thereon while having a reduced complexity of motion. In ionimplantation, the system should mechanically scan the wafer through theion beam at a constant angle of incidence while maintaining the iondosage reaching the wafer surface at relatively constant values.

SUMMARY OF THE INVENTION

It is a feature of the present invention to provide a substratepositioning system to facilitate the performing of certain processing onthe substrate, such as ion implantation. It is another feature toprovide such a system with rotatable members synchronized to form arobotic unit to efficiently and accurately move the substrate to adesired range of motion. It is yet another feature to provide such asystem with a base movable linearly along an axis such that the systemmaintains a constant distance of travel for an ion beam incident on thesubstrate as the rotatable members travel in a curved path. It is yetanother feature of the present invention to provide such a system wherethe rotatable members simultaneously rotate to maintain a substantiallyconstant incident angle of the substrate relative to the ion beam. It isyet another feature of the present invention to provide such a systemthat is easy to use, simple in operation, and particularly well suitedfor the proposed usages thereof.

The substrate positioning system of the present invention comprises alinkage rotatably mounted to a base and an end effector member rotatablymounted to the linkage and configured for supporting a substrate. Meansis provided to rotate the linkage and the member simultaneously as arobotic unit to move the substrate to a desired y-axis and z-axislocation to facilitate performing certain processing on the substrate.

In another aspect, the processing performed on the substrate involvesion implantation. A chamber is provided into which an ion beam isentered, the ion beam configured to scan over the width of a substratealong an x-axis. Within the chamber is the linkage attached at a firstrotary axis to the base and the end effector member attached at a secondrotary axis to the linkage, the linkage and end effector member forminga substrate holder to position the substrate. A drive unit ismechanically connected to the linkage to scan the end effector and heldsubstrate through the ion beam substantially in a z-axis direction.Because the end effector member rotates about the second rotary axis asthe linkage rotates about the first rotary axis, a substantiallyconstant angle of incidence of the ion beam on the substrate ismaintained. The system can be further configured with the base beingmovable along the y-axis such that the system maintains a constantdistance of travel for the ion beam incident on the substrate as thelinkage and end effector member travel in a curved path.

Other advantages and components of the present invention will becomeapparent from the following description taken in conjunction with theaccompanying drawings, which constitute a part of this specification andwherein are set forth exemplary aspects of the present invention toillustrate various features thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view an embodiment of the present inventionshowing a substrate mounted to the end effector member.

FIG. 2 is a side elevation view of the present invention according tothe embodiment of FIG. 1.

FIG. 3 is a perspective view of another embodiment of the presentinvention showing the base being movable along a linear slide.

FIG. 4 is a side elevational view of the present invention according tothe embodiment of FIG. 3.

DETAILED DESCRIPTION OF THE INVENTION

The substrate positioning system 10 of the present invention is showngenerally in FIGS. 1 and 2. The system 10 provides a linkage 12rotatably mounted to a base 14 with a first rotary joint 16 at a firstrotary axis 18 and an end effector member 20 rotatably mounted to thelinkage 12 with a second rotary joint 22 at a second rotary axis 24 forproperly positioning a substrate 26 for various processing. The firstrotary axis 18 is located at a proximal end 28 of the linkage 12 and thesecond rotary axis 24 is located at a distal end 30 of the linkage 12.Both axes are aligned in parallel relationship to one another and extendgenerally parallel to the x-axis. Thus, the base 14 extends upward alongthe z-axis and the linkage 12 and end effector member 20 generally movein the y-z plane. Through the synchronized rotation of the linkage 12about the base 14 and the end effector member 20 about the linkage 12,the system 10 acts as a robotic unit to move the substrate 26 to thedesired location, through a known path at desired velocity.

The rotation of the linkage 12 and end effector member 20 about thefirst and second rotary axes 18, 24, respectively, can be accomplishedby various means. The linkage 12 and end effector member 20 may bemechanically coupled using suitable linkages such as belts and pulleys(not shown), or may be independently controlled through motors (notshown) coupled to each of the linkage and the member. If motors areused, they are preferably mounted within the first and second rotaryjoints 16, 22. The linkage 12 is thus extended or contracted relative tothe base 14 and the end effector member 20 is extended or contractedrelative to the linkage 12. The motion of the linkage 12 and member 20is in the y-z plane.

Although the system 10 can be used in a variety of ways, preferably, thesubstrate 26 is fixedly positioned on the end effector member 20 suchthat the system 10 moves the substrate through an ion beam forperforming ion implantation. In this aspect, the end effector member 20has a planar surface 32 upon which the substrate 26, such as asemiconducting wafer, is mounted. The surface 32 is alignedperpendicular to the length of the member 20 extending from the secondrotary axis 24 to the surface 32, as best seen in FIG. 2. The linkage 12is an elongate member having a length sufficient as to move the endeffector member 20 and wafers 26 of various sizes vertically though theion beam path. Mounting of the wafer 26 to the surface 32 is preferablyaccomplished by clamping the wafer thereon. Also, the wafer 26 isgenerally of the type with a surface area in the form of a disk with adiameter and center.

As seen in FIG. 2, the system 10 is contained within an evacuatedenclosure 34 such that an environment conductive to ion beam transportand implantation is provided. The ion beam is introduced into theenclosure 34 from the end of an ion beam transport system 36, which ispreferably at a fixed location and transmits the beam along the y-axistowards the wafer 26. As is known in the art, the ion beam iselectronically scanned across the held wafer 26 along an axis (thex-axis) or in a fan shaped orientation. This provides an ion beamincident on the wafer 26 that is formed as an elongated shape to deliveruniform ion dosage across the width of the wafer in the x-axis, but doesnot provide an ion beam substantially across the wafer height,perpendicular to the x-axis. The movement of the end effector member 20mechanically scans the wafer 26 through the ion beam along an axisperpendicular to the electronically scanned ion beam such that an entirewafer surface 38 may be uniformly ion implanted. The velocities of themechanical scan preferably move the wafer 26 through the ion beam on theorder of at least 10 inches per second.

To ensure that the proper ion dosage is applied to the wafer 26, theplanar surface 32 of the end effector member 20 is maintained at aconstant angle of incidence, or implant angle, with the ion beamthroughout the mechanical scan. The implant angle can be set at anyangle between 0 and 90 degrees depending on the desired ion dosagecharacteristics. This is accomplished by the coordination of therotation of the linkage 12 and end effector member 20. Because therotation of the linkage 12 about the first rotary axis 18 causes thelinkage distal end 30 to rotate, the second rotary axis 24 mustsimultaneously counter-rotate in a synchronous fashion to ensure thatthe end effector member 20 and surface 32 upon which the wafer 26 isaffixed remain properly oriented at the chosen implant angle. The firstand second rotary axes 18, 24 are coordinated to rotate in oppositedirections (clockwise and counter-clockwise) to properly orient the endeffector member 20. Further, the axes 18, 24 rotate with equal butopposite angular magnitude, or degree of rotation, to maintain theconstant implant angle. Motors, belts and pulleys, or other means areimplemented to rotate the linkage 12 and end effector member 20 aboutthe axes 18, 24. Also, logic circuits and/or processors may beelectrically connected to the means for rotating the linkage 12 andmember 20 to accomplish the programmed coordination of the rotation.Additionally, other factors such as the mechanical scan velocity, theion beam current, or the duty cycle of the electronic scan, may beindividually or simultaneously adjusted to provide the proper iondosage.

The vertical component of the mechanical scanning is accomplishedthrough the rotation of the linkage 12 about the base 14, which is astructure with a fixed position relative to the z-axis. The wafer 26 maybe moved several times through the ion beam such that all portions ofthe wafer surface 38 receive the adequate ion beam dosage. The functionof the end effector member 20 is thus to provide a secure platform forthe wafer 26 for orientation at the desired implant angle throughoutthese scans.

In another aspect shown in FIGS. 3 and 4, the base 14 of the system 10may be provided with a means for linearly moving the base 40 such thatthe horizontal distance along the y-axis between the ion beam transportsystem end 36 and the impact point 42 of the beam on the wafer surface38 remains constant throughout the mechanical scan. Preferably, themeans 40 for moving the base 14 is a linear slide that moves within atrack 44. Because rotation of the linkage 12 about the base 14 causesthe linkage distal end 30 and end effector member 20 mounted thereto tofollow a curved path, the wafer surface 38 moves both vertically alongthe z-axis and horizontally along the y-axis. The movement of the linearslide 40 allows the base 14, and thus the linkage 12 and member 20coupled thereto, to counteract the y-axis component of the holder 20rotation and facilitate the translation of the impact point 42 on thewafer surface 38 moving substantially only in the z-axis. The intensityof the ion beam reaching the wafer surface 38 is maintained as thesurface is moved through the beam.

Assuming that the wafer 26 is affixed to the substrate surface 32 suchthat the wafer surface 38 is orthogonal to the end effector member 20length and the ion beam travels in a parallel line with the y-axis, theformula for calculating the necessary linear movement of the base 14, orcorrection factor, can be calculated. First, the necessary beam traveldistance from the ion beam transport system end 36 to the impact point42 on the wafer surface is determined. The base 14 is moved such thatthe wafer 26 is properly positioned for the necessary beam travel. Acorrection factor K is determined by the difference of a constant E1,which is the y-axis distance from the first rotary axis 18 to the beamimpact point 42 on the wafer surface 38 at the starting point of the ionscan, and the y-axis distance E from the first rotary axis 18 of thebase to the beam impact point 42 on the wafer surface 38 as the linkage12 and end effector member 20 are rotated. Thus, the correction factor Kis calculated as:

K=E1−E;

wherein: K is a positive value when the ion beam impact point 42 hasmoved further from the ion beam transport system end 36 and a negativevalue when the beam impact point has moved closer to the beam outputlocation.

If the linkage 12 and the end effector member 20 extend parallel to they-axis, the distance E is determined to be:

E=A+B;

wherein: A is the length of the end effector member 20 from the secondrotary axis 24 to the substrate 26 affixed thereto, plus the thicknessof the substrate; and B is the length of the linkage 12 from the firstrotary axis 18 to the second rotary axis.

When the linkage 12 and end effector member 20 are rotated about thefirst and second rotary axes, 18, 24, respectively, to move thesubstrate 26 through the ion beam, the cosine of the angles formed withthe y-axis must be determined. Thus, for an implant angle of 0 degrees,the distance E is determined by:

E=A(cos Γ)+B(cos θ);

wherein: θ is the angle between the linkage 12 and the y-axis at thefirst rotary axis 18, positively measured above the z-axis; and Γ isangle between the end effector member 20 and the y-axis at the secondrotary axis 24, positively measured above the y-axis. However, because ris equal to the implant angle (because the wafer surface is orthogonalto the end effector length), the value of Γ is zero and the equationreduces to:

E=A+B(cos θ).

The correction factor is then calculated to be:

K=E1−(A+B(cos θ)).

The determination of the correction factor changes when an implant angleof greater than zero but less than 90 degrees is introduced. Thedistance E must not only take into account the relationship between thecosine of the angles formed between the linkage 12 and end effectormember 20 with the y-axis, but also the z-axis position at which the ionbeam impacts the wafer surface 38. To offset from the position of thewafer 26 at the centerline 44 of the end effector length to the beamimpact point 42, the following relationship is observed:

tan (α)=G/F or G=F·tan (α);

wherein: α is the implant angle between the wafer surface 38 and thez-axis measured at the ion beam impact point 42; F is the z-axisdistance from the wafer surface 38 at the centerline of the end effectorlength 44 to the beam impact point; and G is the y-axis distance fromthe wafer surface at the centerline of the end effector length to thebeam impact point. Thus, knowing the implant angle α and the distance F,the distance G can be determined and added to the cosine of the linkageand end effector member angles to determine E. The distance F iscalculated from:

F=C+B(sin θ)+A(sin θ)−D;

Wherein: C is the z-axis distance from a reference x-y plane upon whichthe base 14 is positioned to the first rotary axis 18; and D is thez-axis distance from the reference x-y plane to the ion beam transportsystem end 36. The distance B is calculated from:

E=A(cos Γ)+B(cos θ)+G;

Therefore, E is determined to be:

E=A(cos Γ)+B(cos θ)+tan (α)·[A(sin Γ)+B(sin θ)+C−D];

and the correction factor is then calculated to be:

K=E1−A(cos Γ)+B(cos θ)+tan(α)·[A(sin Γ)+B(sin θ)+C−D].

Knowing the correction factor, logic circuits and/or processors may beelectrically connected to the means 40 for linearly moving the base 14in a y-axis direction such that the base is linearly moved based on thecalculated correction factor to thereby maintain a constant traveldistance for the ion beam from an ion beam transport system end 36 toion beam impact point 42 on the substrate surface 38.

From the foregoing information, it should now be obvious that thesubstrate positioning system 10 provides a simple and efficient solutionfor accurately positioning a substrate to facilitate the performing ofcertain processing on the substrate, such as ion implantation. Thesystem is ideally configured to move the substrate vertically along az-axis through an ion beam scan while reducing or eliminating y-axishorizontal motion of an ion beam impact location on the held substrate.In this way, the proper amount of ion beam dosage is delivered evenlyover the surface of the substrate. It is also to be understood that theterms used herein relating to vertical dimensions along the z-axis andhorizontal dimensions along the y-axis are relative, and the system canbe rotated in any of the x, y, or z axes such that vertical andhorizontal orientations would be changed accordingly. While certainforms of the present invention have been illustrated and describedherein, it is not to be limited to the specific forms or arrangement ofparts described and shown.

What is claimed is:
 1. A substrate positioning system, comprising: alinkage rotatably mounted on a first rotary axis to a base, the baseextending to a fixed height above an x-y reference plane; an endeffector member rotatably mounted on a second rotary axis to a mountingportion of the linkage, the end effector member configured forsupporting a substrate thereto; and means for rotating the linkage aboutthe first rotary axis; wherein the rotation of the linkage about thefirst axis causes movement of the mounting portion of the linkage andsubstantially positions the end effector member and substrate at aspecific y-axis and z-axis location to facilitate ion implantation byscanning the substrate with an ion beam traveling generally in a y-axisplane.
 2. The positioning system of claim 1, wherein a means forperforming processing on the substrate is positioned at a fixed locationrelative to the x-y reference plane.
 3. The positioning system of claim1, wherein the rotating means is mechanically connected to the linkage.4. The positioning system of claim 1, wherein the end effector member ispositioned as to maintain a constant angle between a surface of thesubstrate and the z-axis.
 5. The positioning system of claim 4, whereinthe first rotary axis is configured to rotate in a direction opposite ofthe second rotary axis as to maintain a constant angle between a surfaceof the substrate and the z-axis.
 6. The positioning system of claim 5,wherein the first rotary axis is configured to rotate with the sameangular magnitude as the second rotary axis.
 7. The positioning systemof claim 1, wherein the linkage has a proximal end and a distal end, thelinkage being mounted to the base at the proximal end and the endeffector member being mounted to the distal end.
 8. The positioningsystem of claim 1, wherein the means for rotating the linkage is furthermechanically connected to the end effector member to rotate the endeffector member about the second rotary axis and thereby position theend effector member and the substrate at a specific y-axis and z-axislocation for performing processing on the substrate.
 9. The positioningsystem of claim 8, wherein the means for rotating the linkage isconfigured to maintain a constant angle between a surface of thesubstrate and the z-axis.
 10. The positioning system of claim 1, furthercomprising a second means mechanically connected to the end effectormember to rotate the member about the second rotary axis to position themember and the substrate at a specific y-axis and z- axis location forperforming processing on the substrate.
 11. The positioning system ofclaim 10, wherein the second means for rotating the end effector memberis configured to maintain a constant angle between a surface of thesubstrate and the z-axis.
 12. The positioning system of claim 1, whereinthe means for rotating the linkage comprises a motor.
 13. Thepositioning system of claim 1, wherein the substrate is a semiconductingwafer.
 14. The positioning system of claim 1, further comprising a meansfor linearly moving the base in a y-axis direction to maintain aconstant travel distance for the ion beam from an ion beam transportsystem end to an impact point of the beam with the substrate while thelinkage is being rotated to position the substrate at a specific z-axislocation.
 15. The positioning system of claim 14, wherein the endeffector member is positioned as to maintain a constant implant anglefor the ion beam with a surface of the substrate, and the movement ofthe base to maintain a constant travel distance for the ion beam isdetermined by the equation or the relation substantially equivalentthereto: K=E1−A(cos Γ)+B(cos θ)+tan (α)·(A(sin Γ+B(sin θ)+C−D), whereinK: a correction factor to determine the linear distance of travel of thebase necessary to maintain a constant travel distance for the ion beam,E1: a constant y-axis distance measured from the first rotary axis ofthe base to the ion beam impact point on the substrate when thesubstrate is positioned at the desired distance from ion beam outputlocation, the first rotary axis being an x-axis, A: a length of the endeffector member from the second rotary axis to the substrate affixedthereto plus the thickness of the substrate, the second rotary axisbeing an x-axis, B: length of the linkage from the first rotary axis ofthe base to the second rotary axis, the first rotary axis being anx-axis, C: a z-axis distance from a reference x-y plane upon which thebase is positioned to the first rotary axis, D: a z-axis distance fromthe reference x-y plane to the ion beam output location, θ: an anglebetween the linkage and the z-axis at the first rotary axis, positivelymeasured above the z-axis, Γ: an angle between the end effector memberand the z-axis at the second rotary axis, positively measured above thez-axis, and α: an ion implant angle between the substrate surface andthe z-axis measured at the ion beam impact point and having a fixedvalue between 0 and 90 degrees.
 16. An ion implantation apparatus,comprising: a chamber into which an ion beam is entered, the ion beambeing configured for scanning over the width of a substrate along anx-axis, the ion beam being configured to travel generally in a y-axisthe substrate being positioned in the chamber; a substrate holdercomprising a linkage and an end effector member, the linkage having aproximal end with a first rotary axis and a distal end with a secondrotary axis, the first rotary axis attached to a base and the secondrotary axis attached to the end effector member, the substrate holderpositioning the substrate in the chamber; a drive unit mechanicallyconnected to the linkage to move the substrate through the ion beamsubstantially in a direction along a z-axis perpendicular to thedirection of the ion beam scan; and a means for linearly moving the basein a y-axis direction to maintain a constant travel distance for the ionbeam from an ion beam transport system end to an impact point of thebeam with the substrate while the substrate holder is being rotated tomove the substrate through the ion beam more precisely in a directionalong the z-axis; wherein the end effector member is configured torotate about the second rotary axis as the linkage rotates about thefirst rotary axis to maintain a substantially constant implant angle ofthe substrate relative to the ion beam.
 17. The apparatus of claim 16,wherein variations of the dose of the ion beam reaching the substrate,caused by the changing distance the ion beam has to travel along they-axis to reach the substrate due to the rotation of the end effectormember, are avoided by calculating a correction factor and adjusting atleast one of the ion beam current, the duty cycle of the ion beam scan,and the mechanical scan velocity to produce a constant dose of the ionbeam.
 18. The apparatus of claim 16, wherein the first and second rotaryaxes are parallel to the x-axis.
 19. The apparatus of claim 16, whereinthe first rotary axis is configured to rotate in a direction opposite ofthe second rotary axis as to maintain the substantially constant implantangle.
 20. The apparatus of claim 19, wherein the first rotary axis isconfigured to rotate with the same angular magnitude as the secondrotary axis.
 21. The apparatus of claim 16, wherein the drive unit isfurther mechanically connected to the end effector member to aid inmoving the substrate though the ion beam substantially in a directionalong a z-axis perpendicular to the direction of the ion beam scan. 22.The apparatus of claim 16, further comprising an end effector drive unitmechanically connected to the end effector member to move the substratethrough the ion beam substantially in a direction along a z-axisperpendicular to the direction of the ion beam scan.
 23. The apparatussystem of claim 16, wherein the substrate is a semiconducting wafer. 24.The apparatus of claim 16, wherein the substrate is affixed to the endeffector member, and the movement of the base to maintain a constanttravel distance for the ion beam is determined by the equation or therelation substantially equivalent thereto: K=E1−A(cos Γ)+B(cos θ)+tan(α)·(A(sin Γ+B(sin θ)+C−D), wherein K: a correction factor to determinethe linear distance of travel of the base necessary to maintain aconstant travel distance for the ion beam, E1: a constant y-axisdistance measured from the first rotary axis of the base to the ion beamimpact point on the substrate when the substrate is positioned at thedesired distance from ion beam output location, the first rotary axisbeing an x-axis, A: a length of the end effector member from the secondrotary axis to the substrate affixed thereto plus the thickness of thesubstrate, B: length of the linkage from the first rotary axis of thebase to the second rotary axis, C: a z-axis distance from a referencex-y plane upon which the base is positioned to the first rotary axis, D:a z-axis distance from the reference x-y plane to the ion beam outputlocation, θ: an angle between the linkage and the z-axis at the firstrotary axis, positively measured above the z-axis, Γ: an angle betweenthe end effector member and the z-axis at the second rotary axis,positively measured above the z-axis, and α: an ion implant anglebetween the substrate surface and the z-axis measured at the ion beamimpact point and having a fixed value between 0 and 90 degrees.
 25. Amethod for ion implantation on a substrate, comprising the steps of:positioning a substrate on a substrate holder, the holder comprising alinkage and an end effector member, the linkage having a proximal endwith a first rotary axis and a distal end with a second rotary axis, thefirst rotary axis attached to a base and the second rotary axis attachedto the end effector member, the holder being disposed within a chamberinto which an ion beam is entered, the ion beam being configured forscanning over the width of the substrate along an x-axis; translatingthe substrate through the ion beam substantially in a direction along az-axis perpendicular to the direction of the ion beam scan bysimultaneously rotating the linkage at the first rotary axis about thebase and rotating the end effector member at the second rotary axisabout the linkage so as to maintain a substantially constant implantangle of the substrate relative to the ion beam; and moving the baselinearly in a y-axis direction to maintain a constant travel distancefor the ion beam from an ion beam transport system end to an impactpoint of the beam with the substrate while the substrate holder is beingrotated to move the substrate through the ion beam more precisely in adirection along the z-axis.
 26. The method of claim 25, wherein themovement of the base to maintain a constant travel distance for the ionbeam is determined by the equation or the relation substantiallyequivalent thereto: K=E1−A(cos Γ)+B(cos θ)+tan (α)·(A(sin Γ+B(sinθ)+C−D), wherein K: a correction factor to determine the linear distanceof travel of the base necessary to maintain a constant travel distancefor the ion beam, E1: a constant y-axis distance measured from the firstrotary axis of the base to the ion beam impact point on the substratewhen the substrate is positioned at the desired distance from ion beamoutput location, the first rotary axis being an x-axis, A: a length ofthe end effector member from the second rotary axis to the substrateaffixed thereto plus the thickness of the substrate, B: length of thelinkage from the first rotary axis of the base to the second rotaryaxis, C: a z-axis distance from a reference x-y plane upon which thebase is positioned to the first rotary axis, D: a z-axis distance fromthe reference x-y plane to the ion beam output location, θ: an anglebetween the linkage and the z-axis at the first rotary axis, positivelymeasured above the z-axis, Γ: an angle between the end effector memberand the z-axis at the second rotary axis, positively measured above thez-axis, and α: an ion implant angle between the substrate surface andthe z-axis measured at the ion beam impact point and having a fixedvalue between 0 and 90 degrees.
 27. The method of claim 25, wherein thesubstrate is a semiconducting wafer.